How to Solve a Sudoku

Sudoku is a logic puzzle where you fill a 9×9 grid with numbers from 1 to 9. The goal is to place each number so that every row, column, and 3×3 box contains each number exactly once. With a few simple rules and logical solving techniques, you can solve Sudoku puzzles without guessing.

This guide explains how to play Sudoku, how to read the puzzle, and the best Sudoku solving strategies for beginners. Once you understand the basic rules and elimination techniques, even more challenging Sudoku puzzles become much easier to solve.

What Is Sudoku?

Sudoku is a number-based logic puzzle played on a 9×9 grid. The grid is divided into nine smaller 3×3 boxes. Some numbers are already filled in, while the remaining squares are empty.

The objective is to fill every empty square with a number from 1 to 9 while following the Sudoku rules. Each number can appear only once in every row, column, and 3×3 box.

Sudoku does not require mathematical calculations. It is a logic puzzle that can be solved by identifying possible numbers and eliminating numbers that cannot fit.

How Do Sudoku Rules Work?

Understanding the basic rules is the most important part of learning how to solve Sudoku.

Every row must contain the numbers 1 through 9 exactly once. The same rule applies to every column and every 3×3 box.

For example, if a row already contains the numbers 1, 2, 3, 5, 6, 7, 8, and 9, the only missing number is 4. Therefore, the empty square must contain 4.

The same type of deduction can be used with columns and 3×3 boxes. Every empty square has a limited set of possible numbers based on the numbers already present in its row, column, and box.

Sudoku Rules

Before solving your first puzzle, remember these basic Sudoku rules:

• Every row must contain the numbers 1 through 9 exactly once.
• Every column must contain the numbers 1 through 9 exactly once.
• Every 3×3 box must contain the numbers 1 through 9 exactly once.
• A number cannot appear more than once in the same row.
• A number cannot appear more than once in the same column.
• A number cannot appear more than once in the same 3×3 box.
• Every empty square must eventually contain one number from 1 through 9.

The key to solving Sudoku is elimination. Instead of trying random numbers, use the existing numbers in the puzzle to determine which numbers cannot go into each empty square.

How to Solve a Sudoku Step by Step

1. Start With Rows, Columns, or Boxes With the Most Numbers

Begin with rows, columns, or 3×3 boxes that already contain many numbers. These areas usually have fewer missing numbers, making them easier to solve.

For example, if a row contains eight numbers and has only one empty square, the missing number can be determined immediately.

You should also look at boxes that are nearly complete. A 3×3 box with only one or two empty squares can often provide several useful deductions.

2. Look for Missing Numbers

One of the simplest Sudoku techniques is to identify which numbers are missing from a row, column, or 3×3 box.

Suppose a row contains: 1, 2, 3, 5, 6, 7, 8, 9. The only missing number is 4, so the empty square must contain 4.

This technique is especially useful at the beginning of a Sudoku puzzle when several rows, columns, or boxes are almost complete.

3. Use Elimination to Find Possible Numbers

When an empty square cannot be solved immediately, determine which numbers are allowed to go there.

Check the square's row, column, and 3×3 box. Any number that already appears in one of those three areas cannot be placed in the empty square.

For example, if a square's row already contains 1, 2, 5, and 8, its column contains 3 and 6, and its box contains 4 and 7, then every number from 1 through 8 is eliminated. The only possible number is 9.

This process of eliminating impossible numbers is one of the most important Sudoku solving techniques.

4. Find Naked Singles

A naked single is an empty square where only one possible number remains after checking its row, column, and 3×3 box.

If an empty square can only contain the number 7, then 7 must be placed there. Once the number is filled in, it may create new opportunities in the surrounding row, column, and box.

Look for these single-candidate squares regularly as you work through the puzzle.

5. Find Hidden Singles

Sometimes a square has several possible numbers, but one particular number can only appear in one empty square within a row, column, or 3×3 box. This is called a hidden single.

For example, a 3×3 box may be missing the numbers 2, 5, and 8. If only one of its empty squares can contain 8, then that square must contain 8.

Hidden singles are especially useful when a puzzle becomes more difficult and simple missing-number deductions are no longer enough.

6. Use the 3×3 Boxes to Narrow Down Numbers

The smaller 3×3 boxes provide important information that can help solve both rows and columns.

If a number can only appear in one particular row within a 3×3 box, you can eliminate that number from the other empty squares in the same row outside the box.

This technique is sometimes called box-line elimination. It becomes increasingly useful as the puzzle gets harder.

7. Keep Checking Rows, Columns, and Boxes

Sudoku is solved by constantly using information from all three directions: rows, columns, and 3×3 boxes.

Placing one number can immediately change the possibilities in several nearby squares. After making a deduction, check the affected row, column, and box for new opportunities.

Think of the puzzle as a chain of deductions: row → column → box → row → column.

Understanding Candidate Numbers

Candidate numbers are the numbers that could legally be placed in an empty square based on the current state of the puzzle.

For example, if a square's row already contains 1, 4, and 7, its column contains 2 and 8, and its box contains 3 and 6, the remaining candidates may be 5 and 9.

Candidate notes can be useful when a puzzle becomes difficult. By recording possible numbers in empty squares, you can spot squares that eventually have only one candidate.

As new numbers are placed, remove those numbers from the candidates in the same row, column, and box.

How Sudoku Pairs Work

Another useful technique is identifying pairs of candidates.

If two empty squares in the same row, column, or 3×3 box contain exactly the same two possible numbers, those numbers must occupy those two squares.

For example, if two squares in a row can only contain 2 or 7, then 2 and 7 must be placed in those two squares in some order. As a result, you can eliminate 2 and 7 from the other empty squares in that row.

This technique is known as a naked pair and can help unlock puzzles that cannot be solved using simple singles alone.

Common Sudoku Solving Mistakes

Guessing Too Early

A well-designed Sudoku can be solved through logical deductions. If you find yourself guessing, look again at the rows, columns, and boxes for additional constraints before committing to a number.

Ignoring the 3×3 Boxes

Beginners sometimes focus only on rows and columns. Remember that every number also has to satisfy the rules of its 3×3 box.

Forgetting to Recheck the Puzzle

Every number you place changes the possibilities around it. After making a deduction, check the affected row, column, and box for newly available numbers.

Writing Numbers Without Checking All Three Areas

Before placing a number, make sure it does not already appear in the square's row, column, or 3×3 box. A number must satisfy all three constraints at the same time.

Only Looking for Nearly Complete Rows

Rows with only one missing number are easy to solve, but difficult puzzles often require you to look for hidden singles, candidate restrictions, and box-line interactions as well.

Tips for Solving Sudoku Faster

• Start with rows, columns, and boxes that contain the most numbers.
• Look for areas with only one or two missing numbers.
• Use elimination to determine possible candidates for empty squares.
• Look for naked singles and hidden singles.
• Check 3×3 boxes carefully for restricted number placements.
• Use candidate notes when the puzzle becomes more difficult.
• Look for pairs when simple single-number deductions stop working.
• Recheck affected rows, columns, and boxes after every important deduction.
• Avoid guessing when another logical deduction may be possible.

Sudoku Example

The examples below show how a Sudoku puzzle looks before solving and how the completed grid looks after all of the empty squares have been filled.

What Happens When You Get Stuck?

Getting stuck is normal, especially when solving more difficult Sudoku puzzles. Instead of guessing, return to the rows, columns, and 3×3 boxes and look for squares with limited possibilities.

Check whether a number can only appear in one square within a particular row, column, or box. These hidden singles can often provide the next important deduction.

You can also review your candidate notes. If two squares share the same two candidates, they may form a pair that allows you to eliminate those candidates from other squares in the same area.

Another useful approach is to find the row, column, or box with the fewest unsolved squares. The remaining possibilities may be much more restricted there than elsewhere in the puzzle.

How to Get Better at Sudoku

The best way to improve is to solve Sudoku puzzles regularly. Start with easier puzzles so you can become comfortable with the basic rules and elimination techniques. As your solving skills improve, move on to larger challenges with fewer obvious numbers and more advanced deductions.

Focus on solving logically rather than guessing. Over time, you will begin to recognize singles, restricted candidates, pairs, and box-line patterns much faster.

Play Sudoku Online

Ready to try these techniques? Play a free Sudoku puzzle online and use logic and deduction to complete the grid.

You can start with an easier puzzle and work your way up to more difficult Sudoku puzzles as you gain experience.

Choose your preferred difficulty to get started:

• Easy Sudoku Puzzles – Perfect for beginners learning the basics of Sudoku. Use logic and deduction to fill the 9×9 grid with numbers from 1 to 9, ensuring that each number appears only once in every row, column, and 3×3 box.
• Medium Sudoku Puzzles – Challenge yourself with puzzles that require more careful reasoning, improved number recognition, and strategic thinking to complete the grid.
• Hard Sudoku Puzzles – Test your Sudoku skills with challenging puzzles that demand advanced logical deduction, patience, and careful analysis to uncover the correct solution.

Start with Easy to learn the fundamentals, then progress to Medium and Hard as you sharpen your logical thinking, improve your problem-solving skills, and master the challenge of solving Sudoku puzzles.

Frequently Asked Questions About Sudoku

What is Sudoku?

Sudoku is a logic puzzle played on a 9×9 grid divided into nine 3×3 boxes. The goal is to fill every empty square with numbers from 1 through 9 so that each number appears exactly once in every row, column, and 3×3 box.

How do you solve Sudoku?

Start by looking for rows, columns, and 3×3 boxes with many numbers already filled in. Identify the missing numbers and eliminate candidates that cannot fit based on the surrounding row, column, and box.

Do Sudoku puzzles require guessing?

No. Standard Sudoku puzzles can be solved using logical deductions. When you get stuck, look for hidden singles, restricted candidates, pairs, and other logical relationships instead of guessing.

What is a 3×3 box in Sudoku?

A 3×3 box is one of the nine smaller sections that make up a standard 9×9 Sudoku grid. Each box must contain the numbers 1 through 9 exactly once.

What is the easiest way to solve Sudoku?

Start with rows, columns, and boxes that are nearly complete. Find missing numbers, eliminate impossible candidates, and look for squares where only one number can fit. Then repeat the process as each new number creates additional deductions.

Can I play Sudoku online?

Yes. You can play Sudoku online and practice the solving techniques explained in this guide.